Min[Subscript[x, 1], Subscript[x, 2], Subscript[x, 3]] == Subscript[x, 1] /; Element[Subscript[x, 1], Reals] && Element[Subscript[x, 2], Reals] && Element[Subscript[x, 3], Reals] && Subscript[x, 1] <= Subscript[x, 2] && Subscript[x, 1] <= Subscript[x, 3]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> min </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mn> 3 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &#8804; </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &#8804; </mo> <msub> <mi> x </mi> <mn> 3 </mn> </msub> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <min /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <reals /> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <reals /> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 3 </cn> </apply> <reals /> </apply> <apply> <leq /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <leq /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Min", "[", RowBox[List[SubscriptBox["x_", "1"], ",", SubscriptBox["x_", "2"], ",", SubscriptBox["x_", "3"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubscriptBox["xx", "1"], "/;", RowBox[List[RowBox[List[SubscriptBox["xx", "1"], "\[Element]", "Reals"]], "&&", RowBox[List[SubscriptBox["x", "2"], "\[Element]", "Reals"]], "&&", RowBox[List[SubscriptBox["x", "3"], "\[Element]", "Reals"]], "&&", RowBox[List[SubscriptBox["xx", "1"], "\[LessEqual]", SubscriptBox["x", "2"]]], "&&", RowBox[List[SubscriptBox["xx", "1"], "\[LessEqual]", SubscriptBox["x", "3"]]]]]]]]]]]

2001-10-29